Neidhardt units, history

A bit of my previous message went missing.
The main advantage of using 'NU' (2-cent or 1/12-Pythagorean-comma
chunks) for considering historical tunings or modern-day work with
'traditional' instruments, is that they have a degree of precision
which is realistic, given the behaviour of the instruments and the
uncertainty of historical investigation. It is also acoustically
reasonable for tempered intervals in many situations: can the
difference between 396 and 398 cents be more than marginally significant?

Aside from Neidhardt himself, and Sorge, who (picky as he was) didn't
seem to consider it worth dividing things any finer than 1/12 comma,
Mark Lindley has used 'NU' extensively in his historical surveys.
Many historical theoretical tuning recipes can be written in simple
whole numbers of 'NU', or at the worst, simple fractions or one place
of decimals for the purpose of avoiding rounding errors in
calculationadding up intervals.

Numbers with a greater degree of precision are in most cases simply
misleading, implying more accurate knowledge of actual sounding
intervals than any historical writer could have.

As I said, theorists can be arbitrarily precise - providing they don't
confound this precision with their knowledge of actual musical
intervals in instruments, either today or 300 years ago...
~~~T~~~

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
>
> A bit of my previous message went missing.
> The main advantage of using 'NU' (2-cent or 1/12-Pythagorean-comma
> chunks) for considering historical tunings or modern-day work with
> 'traditional' instruments, is that they have a degree of precision
> which is realistic, given the behaviour of the instruments and the
> uncertainty of historical investigation. It is also acoustically
> reasonable for tempered intervals in many situations: can the
> difference between 396 and 398 cents be more than marginally
significant?

I would recommend using 612-et, and thereby not distinguishing between
1/12 of a Pythagorean and 1/11 of a Didymus comma.